Does pitchers back foot have to break contact with rubber for him to throw to first?

No. Remember there are left handed pitchers and right handed pitchers.

Almost every umpire will declare a right handed pitcher to have balked if his foot doesn't disengage from the rubber when he throws to first.

A left handed pitcher simply steps and throws to first. His back foot usually never disengages from the rubber.

To over simplify - a pitcher is called for a balk when the umpire judges the pitcher to have deceived the runner in some way. So, anytime a baulk is called, an umpire made a judgement call.